Wednesday, 23 November 2011

In this post, I'll to give an overview of the HACD parameters and explain their meaning and how they should be set. The text will be improved over time. My main concern is to have things written down for reference...

Parameters overview

Parameter

Description

Default

NTargetTrianglesDecimatedMesh

Target
number of triangles in the decimated mesh. The decimation stage was added
mainly to decrease the computation costs for dense meshes (refer to Section 2.1).

1000

NVerticesPerCH

Maximum number
of vertices in the generated convex-hulls.

100

ScaleFactor

Normalization
factor used to ensure that the
other parameters (e.g. concavity) are expressed w.r.t. a fixed size. Refer to Section 2.3 for details

1000

SmallClusterThreshold

Threshold on
the clusters area (expressed as a percentage of the entire mesh area) under
which the cluster is considered small and it is forced to be merged with
other clusters at the price of a high concavity.

0.25

AddFacesPoints

If enabled an additional
ray located at the center of each triangle pointing toward its normal is
considered when computing the concavity of a non-flat cluster. The parameter was
added to handle coarse meshes (i.e. with a low number of vertices)

ON

AddExtraDistPoitns

If enabled additional
rays are considered to handle bowl-like shapes.

ON

NClusters

Minimum number of
convex-hulls to be generated

1

Concavity

Maximum allowed
concavity

100

ConnectDist

If the distance
between two triangles, each belonging to a different connected components (CCs),
is lower than the ConnectDist threshold an additional edge connecting
them is added to the dual graph. This parameter was added to handle meshes
with multiple CCs.

30

VolumeWeight

Weight
controlling the contribution of the volume related cost to the global
edgecollapse cost (refer to XXX for details).

0.0

(not used)

CompacityWeight

Weight
controlling the contribution of the shape factor related cost to the global
edgecollapse cost (refer to XXX for details).

0.0001

FlatRegionThreshold

Threshold expressed
a percentage of ScaleFactor under which a cluster is considered flat.

1

ComputationWeight

Weight
controlling the contribution of the computation related cost to the global
edgecollapse cost (refer to XXX for details).

0.01

2. Detailed description

NTargetTrianglesDecimatedMesh

In order to reduce the computations times for dense meshes, the HACD library makes it possible to decimate the original mesh before running the decomposition process. More details about the decimation algorithm are provided here http://kmamou.blogspot.com/2011/10/hacd-optimization.html

NVerticesPerCH

this parameter was introduced in order to comply with the constraints that most physics engines put on the number of vertices/triangles per convex-hull (CH). If the function HACD::Compute() is called with the parameter fullCH=false, then the generated CHs will have a number of vertices lower than NVerticesPerCH.

In order to optimally choose the best vertices to keep in the final CH, the ICHull::Process(unsigned long nPointsCH) function implements a slightly different version of the Incremental Convex Hull algorithm (cf. democode ). Here, at each step, the point with the highest volume increment is chosen, until all points are processed or the CH has exactly NVerticesPerCH points.

A normalization process is applied to the input mesh in order to ensure that the other parameters (e.g. concavity) are expressed w.r.t. a fixed size. This process is inverted before producing the final CHs.

The HACD::Compute() function follows the following main steps:

bool HACD::Compute(bool
fullCH, bool exportDistPoints)

{

if (m_targetNTrianglesDecimatedMesh > 0)

{

DecimateMesh(targetNTrianglesDecimatedMesh);

}

NormalizeData();

CreateGraph();

InitializeDualGraph();

InitializePriorityQueue();

Simplify();

DenormalizeData();

CreateFinalCH();

returntrue;

}

The HACD::NormalizeData() function centers the mesh and scale it so its coordinates are in the interval [-m_sacle, m_sclae]x[-m_sacle, m_sclae]x[-m_sacle, m_sclae]. The code proceeds as follows:

void HACD::NormalizeData()

{

const Real
invDiag = static_cast<Real>(2.0 * m_scale
/ m_diag);

for (size_t v = 0; v < m_nPoints ; v++)

{

m_points[v]
= (m_points[v] - m_barycenter) * invDiag;

}

}

The HACD::DenormalizeData() function invert the normalization operated by HACD::NormalizeData():

void HACD::DenormalizeData()

{

const
Real diag = static_cast<Real>(m_diag /
(2.0 * m_scale));

for
(size_t v = 0; v < m_nPoints ; v++)

{

m_points[v] = m_points[v] * diag +
m_barycenter;

}

}

SmallClusterThreshold

Due to numerical stability issues (or maybe some bugs I haven't spotted yet :) ) the HACD algorithm may produce small clusters. In order to detect them and make sure they will be merged, the SmallClusterThreshold was introduced. A cluster is considered to be small if its area is smaller than SmallClusterThreshold% of the entire mesh area.

The condition2 in the HACD::Simplify() function forces small clusters to be merged (m_area is the area of the entire mesh):

The parameter AddFacesPoints was introduced to improve the precision of the concavity computation for meshes with a low number of vertices. The idea is to add additional rays located each at the center of a triangle and pointing to the same direction as its normal.

The Parameter AddExtraDistPoints was added to handle bowl-like shapes. As illustrated below, if only the rays located on the current cluster are considered when computing its concavity, you may end up with a big cluster corresponding to the external surface (which is convex) of the bowl containing a lot of small clusters located on the internal part (which is concave).

Bad decomposition for bowl-like shapes if AddExtraDistPoints is not enabled

In order to avoid such a bad decomposition, the idea consists in introducing new rays that would constrain the propagation of the cluster corresponding to the external surface of the bowl by taking into account rays located on the concave part. More precisely, during the initialization stage, an additional ray (the yellow ray in the figure below) is associated with each triangle (colored in red).

The additional ray, denoted R (the yellow arrow), is defined as follows. Let N be the normal (the blue arrow) to the current triangle T (colored in red) and X be the ray starting at the center of T and with direction (-N) (the dotted green arrow). The starting point of R, denoted P0 (the yellow point), is defined a the nearest intersection point of X and the mesh. Moreover, the normal of the surface at P0 should point to the same direction as X. R has the direction of the normal of the surface at the P0.

Additional ray (yellow) is associated with the red triangle when AddExtraDistPoints is activated

In order to handle meshes with different connected components. The idea consists in adding "virtual edges" between triangles belonging to different CCs. More precisely, if the distance between two triangles T1 and T2 belonging each to a different CC is lower than a threshold distConnect then an edge connecting T1 to T2 is added to the dual graph.

When computing concavity we need to distinguish between flat surfaces and non-float surfaces. The measure of flatness considered in HACD is related to the ratio between the convex-hull volume and the area of its boundary. If this later ration is small compared to m_scale then the mesh is considered flat. Otherwise it is considered non-flat. The parameter FlatRegionThreshold is the threshold which separate flat region from non flat region. It is expressed as percentage of m_scale.

In practice, the final concavity is computed as weighted sum of the flat region concavity and the 3D concavity. The weight is a function of the flatness of the cluster.